Using the information in Table 7-1 and the simplified relations of Table 7-2, devise a simplified relation that may be used as a substitute for Equation (7-50) to calculate free convection from a sphere to air at 1 atm.

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Equation 7-50
Nuf = 2 + 0.43(Grf Prf)1/4

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Table 7-1I Constants for use with Equation (7-25) for isothermal surfaces. Geometrv Grf Prf Reference(s) In Vertical planes and cylinders 10-1-104 Use Fig. 7-5 Use Fig. 7-5 4 10°-1013 109-1013 0-10-5 10-5-104 0.59 0.021 0.10 0.4 30 22, 16 4 Horizontal cylinders Use Fig. 7-6 Use Fig. 7-6 4 0.53 109-1012 10-10-10-2 10-2-102 102-104 104-107 107-1012 0.675 1.02 0.850 0.480 0.125 0.54 4 4 767 76T 76 76 76 0.058 0.148 0.188 Upper surface of heated plates 2 x 104-8 x 106 44, 52 or lower surface of cooled plates 0.15 Upper surface ofheated plates Lower surface of heated plates Vertical cylinder, 8x106-1011 105-1011 104-106 44, 52 or lower surface of cooled plates 0.27 44, 37, 75 or upper surface of cooled plates 0.775 0.21 height diameter characteristic length- diameter Iregular solids, characteristic 104-109 0.52 78 length- distance fiuid particle travels in boundary layer Turbulent, Surface AT /4 h1.31 (AT)1/3 Vertical plane or cylinder Horizontal cylinder Horizontal plate Heated plate facing upward or h1.42 AT 1/4 に1.24(AT)1/3 h-1.32 h 1.52(AT)1/3 cooled plate facing downward cooled plate facing upward side, Area-612 1/4 AT Heated plate facing downward or AT Heated cube: L = length of h = 1.052 where h = heat-transfer coefficient, W/m2·°C L= vertical or horizontal dimension. m d= diameter, m